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Vortical Analysis of Secondary Flows in Turbine Cascades
P M V SubbaraoProfessor
Mechanical Engineering Department
A Pictorial Fluid Mechanics for Complex Flows……
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Formation & Evolution of Endwall Flows
• The picture of endwall flows in turbine blade-to-blade passages is extremely complex.
• The secondary flows also modify the shape of endwall boundary layers from which they originate.
• Demands a set of creative thinking to understand the development of secondary flows.
• A creative thinker will always tend to propose a geometrical solution the complex problem.
• How to proceed to understand this phenomena?
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Hans Albert Einstein (May 14, 1904 – July 26, 1973)
• Hans Albert Einstein was a Swiss-American engineer and educator
• He was an avid sailor, frequently taking colleagues and family out for excursions on the San Francisco Bay.
• On his many field trips and academic excursions, he took thousands of pictures, many of which he developed himself and presented as slide shows.
• In tribute to Einstein's lifelong contributions to the field, his former graduate students published a book of research in his honor in 1972, Sedimentation: Symposium to Honor Professor H.A. Einstein.
• In 1988, the American Society of Civil Engineers created the Hans Albert Einstein Award to recognize outstanding achievements in erosion control, sedimentation and/or waterway development.
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Theory of Formation of endwall flows
• The main type of secondary flow is the induced recirculating flow, which leads to the formation of a passage vortex.
• The source of the induced recirculating flow is the cross flow in the endwall boundary layer.
The passage vortex forms as a result of force equilibrium in curvilinear motion. The momentum equation in the cross-stream direction can be written in the form:
n
p
R
vcf
2
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The Reaction
• With a decrease of the radial velocity in the boundary layer, a reduction of the streamline curvature radius in the boundary layer flow is required in order to balance the pitch-wise pressure gradient formed in the channel.
• As a consequence, the boundary layer flow is turned more than the main flow in the blade-to-blade channel, leading to a crossflow from the pressure to suction surface in the endwall boundary layer.
• A compensating return flow must then occur at a certain distance from the endwall, giving rise to the recirculating flow.
• The action is science but reaction is an engineering art.
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Secondary flow models in turbine cascades
Model (a) : model of Hawthorne (1955)
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Secondary flow models in turbine cascades
Model (b) : Model of Langston (1980)
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Secondary flow models in turbine cascades
Model (c) : model of Sharma and Butler (1987)
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Secondary flow models in turbine cascades
Model (d) : model of Goldstein and Spores (1988)
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Secondary flow models in turbine cascades
Model (e) : model of Doerffer and Amecke (1994)
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Secondary flow models in turbine cascades
Model (f) : model of Wang et al. (1997)
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Secondary whirl
Describe Secondary Flow as An Elephant !?!?!
The main type of secondary flow is the induced recirculating flow, which leads to the formation of a passage vortex.
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Generation of Secondary Flow System
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Horse-shoe vortex
• Another element of secondary flows is a horse-shoe vortex.
• The process of formation of the horse-shoe vortex upstream of the leading edge and its downstream transport was explained by many researchers.
• The models of the process of formation of horse shoe presented in these papers differ from one another in details only.